Coset codes. I. Introduction and geometrical classification

• Authors: G. D. Forney, Jr.
• Venue: IEEE Transactions on Information Theory - Part 1
• Year: 2006

Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Λ/Λ' and by a binary encoder C that selects a sequence of cosets of the lattice Λ'. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by C Λ/Λ'. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters